(Work in progress with O. Bandtlow). We consider uniformly expanding interval maps that are Markov. Introducing a finite number of holes, restricting the map to the remaining set we show that the entropy of the restricted map is Hölder continuous with respect to the hole position and size under a non-degeneracy condition. The Hölder exponent is related to the entropy itself and expansion rates of the map. Examples and counter-examples, with numerics illustrates the result.